Sounds like quite a process, but folks here are helpful and I'm sure we'll get you through this. I lived in Stoneham before I moved south, so I am familiar with Peabody. (I made the mistake of pronouncing it PEE-bod-ee the first time and was quickly corrected. It's PEE-bah-dee but pronounced fast like its a single syllable.)
I'm going to send you a PM with my email address. If you email me your house address, I can look on Google Maps and get a satellite image of your property which I can then use to make a scale drawing of your property and how it relates to your neighbors' properties. If Peabody has their zoning maps online, I can also get that information from their website.
They want to know how you plan to care for the chickens so you'll want to know what kind of bedding will be used in the coop, how and how often you'll be cleaning it, and what you plan to do with the poop and dirty bedding. Will you be composting it or disposing of it in the trash? I think flies and smell is the concern here.
For food storage, consider metal trash cans. Metal cans are impervious to gnawing rodents. The consideration here is rats.
For the location in the yard, do you know what the setback requirements are? The consideration here is that you don't put the coop too close to the neighbor's property and too close to their house which would make a nuisance for them.
They notify the neighbors and give them time to object. Usually it's only abutters that are given the opportunity to object. If you have a good relationship with your abutting neighbors and you can show that you have plans that will eliminate the introduction of flies, smells and rats to your yard and the neighbor's properties, you should be okay.
